HORIZON-OPTIMIZED WEIGHTS FOR FORECAST COMBINATION WITH CROSS-LEARNING

ABSTRACT

Recent empirical results show that forecast combinations and cross-learning schemes are winning approaches in the time series field. Although many competition-winning combination methods - with cross-learning or not - use static weights along the forecasting horizon, we could not find extensive work about the effects of using horizon-optimized weights. This paper proposes a forecast combination framework and provides a considerably sizeable empirical investigation into the use of horizon-optimized weights, i.e., weights that may vary over the forecasting horizon. We build on cross-learning, time series clustering and cross-validation to form Horizon-Optimized Convex Combinations (HOC2) of forecasts from five methods: Automated exponential smoothing, Automated ARIMA, Theta, TBATS, and Seasonal naïve. Our combinations were tested with data from the previous M1, M3 and M4 forecast competitions, comprising 104,004 time series with different frequencies and lengths. The results shall be helpful to support future research on how horizon-optimized weights can be used interchangeably with static ones.

Keywords:
forecast combinations; convex combinations; cross-learning; time series clustering; cross-validation; M competitions